# Near and far field

The near field (or near-field) and far field (or far-field) and the transition zone are regions of time varying electromagnetic field around any object that serves as a source for the field. The different terms for these regions describe the way characteristics of an electromagnetic (EM) field change with distance from the charges and currents in the object that are the sources of the changing EM field. The more distant parts of the far-field are identified with classical electromagnetic radiation.

The basic reason an EM field changes in character with distance from its source is that Maxwell's equations prescribe different behaviors for each of the two source-terms of electric fields and also the two source-terms for magnetic fields. Electric fields produced by charge distributions have a different character than those produced by changing magnetic fields. Similarly, Maxwell's equations show a differing behavior for the magnetic fields produced by electric currents, versus magnetic fields produced by changing electric fields. For these reasons, in the region very close to currents and charge-separations, the EM field is dominated by electric and magnetic components produced directly by currents and charge-separations, and these effects together produce the EM "near field." However, at distances far from charge-separations and currents, the EM field becomes dominated by the electric and magnetic fields indirectly produced by the change in the other type of field, and thus the EM field is no longer affected (or much affected) by the charges and currents at the EM source. This more distant part of the EM field is the "radiative" field or "far-field," and it is the familiar type of electromagnetic radiation seen in "free space," far from any EM field sources (origins).

The far-field thus includes radio waves and microwaves several wavelengths from most types of antennas, as well as all the shorter-wave EM radiation in the electromagnetic spectrum (infrared, light, UV, X-rays, etc.). The latter types of EM radiation in normal experience show far-field behavior almost exclusively, due to their shorter wavelength that gives them a "far-field" character at all but extremely short distances from their sources. For example, visible light shows far-field behavior at all distances larger than one micrometer from its source. The wavelengths of visible light is in the range 0.4 to 0.7 micrometers, so the near field for light is in the expected range.

In practical mathematical terms, the dominance of far-field behavior with sufficient distance from the source appears because both currents and the oscillating charge-distributions in antennas (and other radiators) produce dipole type field behavior. While these dipole near-field intensities may be very powerful near the source, they decay very rapidly with distance in comparison to EM radiation (the far-field). Radiative far-field intensity decays more slowly with distance, following the inverse square law for total EM power that is typical of all electromagnetic radiation. For this reason, the far-field component of the EM field wins out in intensity with increasing distance. Thus, for objects such as transmitting antennas, electrical or electronic equipment, dielectric materials, or where radiation is scattering from an object, the non-radiative 'near field' components of electromagnetic fields dominate the EM field close to the object, while electromagnetic radiation or 'far field' behaviors dominate at greater distances. The near-field does not suddenly end where the far-field begins—rather, there is a transition zone between these types where both types of EM field-effects may be significant.

## Regions and their cause

The near-field and far-field of an antenna or other isolated source of electromagnetic radiation are regions around the source. The boundary between the two regions is only vaguely defined, and it depends on the dominant wavelength (λ) emitted by the source.

The far-field is the region in which the field acts as "normal" electromagnetic radiation. The power of this radiation decreases as the square of distance from the antenna, and absorption of the radiation has no effect on the transmitter. Absorption of radiation from the reactive part of the near-field, however, does affect the load on the transmitter. Magnetic induction (for example, in a transformer) can be seen as a very simple model of this type of near-field electromagnetic interaction.

Because each part (electric and magnetic) of the EM field in the far-field region is "produced by" (or associated with) a change in the other part, the ratios of electric to magnetic field strength are fixed and unvarying in the far-field. However, in the near field, the electric and magnetic fields are nearly independent of each other, and each one cannot be calculated from knowing the other (thus, they must be independently measured in the near-field). Depending on the type of source, the near-field will be dominated by either a magnetic component, or an electric component.

Near-fields are dominated by dipole-type electric or magnetic fields. Magnetic near-field components due to changing currents must be of a dipole nature since magnetic "charges" (magnetic monopoles) do not exist. Although electric charges do exist and may create static electric fields, the oscillating electric part of EM near-fields that is created by an electric potential in the radiator always shows a dipole nature, because the source of the electric part of the EM near-field is created from an electrical neutral conductor only in a way that temporarily creates a dipole or multipole. This is because the positive and negative charges in a radiating source have no way to leave it, and are separated from each other by the excitation "signal" (a transmitter or other EM exciting potential) only temporarily. A classic example of this behavior is a radio antenna, which on average over time is electrically neutral, and differs from this state only by temporarily becoming an electrical dipole (or multipole) under the influence of the signal from the transmitter, which separates charges within it for brief periods only. [If an antenna has a static charge, it cannot contribute to the electrical near-field in any way that varies in time, and the same is true for any constant currents that may flow in an antenna].

In the far-field, the shape of the antenna pattern is independent of distance and the angular field distribution is in essence independent of distance from the source. The far-field is also frequently referred to as the "radiation zone", or "free space". A more precise definition is given by the propagation properties. The radiation zone is important because far-fields in general fall off in amplitude by 1∕r. This means that the total energy per unit area at a distance r is proportional to 1∕r2. The area of the sphere is proportional to r2, so the total energy passing through the sphere is constant. This means that the far-field energy actually escapes to infinite distance (it radiates). In general, the purpose of antennas is to communicate wirelessly for long distances using far-fields, and this is their main region of operation (however, certain antennas specialized for near-field communication do exist).

## Definitions

The term "near-field region" (also known as the "near-field" or "near-zone") has the following meanings with respect to different telecommunications technologies:

• The close-in region of an antenna where the angular field distribution is dependent upon the distance from the antenna.
• In the study of diffraction and antenna design, the near-field is that part of the radiated field that is below distances shorter than the Fresnel parameter[1] from the source of the diffracting edge or antenna of longitude or diameter D.
• In optical fiber communications, the region close to a source or aperture.

Because of these nuances, special care must be taken when comprehending the literature about near-fields and far-fields.

### Regions according to electromagnetic length

#### Electromagnetically short antennas

Antenna field regions for antennas that are equal to, or shorter than, one-half wavelength of the radiation they emit, such as the whip antenna of a citizen's band radio, or the antenna in an AM radio broadcast tower.

For antennas shorter than half of the wavelength of the radiation they emit (i.e., "electromagnetically short" antennas), the far and near regional boundaries are measured in terms of a simple ratio of the distance r from the radiating source to the wavelength λ of the radiation. For such an antenna, the near-field is the region within a radius (rλ), while the far-field is the region for which r ≫ 2λ. The transition zone is the region between r = λ and r = 2λ.

Note that D, the length of the antenna is not important, and the approximation is the same for all shorter antennas (sometimes ideally called "point antennas"). In all such antennas, the short length means that charges and currents in each sub-section of the antenna are the same at any given time, since the antenna is too short for the RF transmitter voltage to reverse before its effects on charges and currents are felt over the entire antenna length.

#### Electromagnetically long antennas

For antennas physically larger than a half-wavelength of the radiation they emit, the near and far fields are defined in terms of the Fraunhofer distance. The Fraunhofer distance, named after Joseph von Fraunhofer, is the value of:

$d_{\rm f} = {{2D^2}\over{\lambda}},$

where D is the largest dimension of the radiator (or the diameter of the antenna) and λ is the wavelength of the radio wave. This distance provides the limit between the near and far field. The parameter D corresponds to the physical length of an antenna, or the diameter of a "dish" antenna.

Having an antenna electromagnetically longer than one-half the dominated wavelength emitted considerably extends the near-field effects, especially that of focused antennas. Conversely, when a given antenna emits high frequency radiation, it will have a near-field region larger than what would be implied by the shorter wavelength.

Additionally, a far-field region distance df must satisfy these two conditions.[2]

$d_{\rm f} \gg D,$
$d_{\rm f} \gg \lambda,$

where D is the largest physical linear dimension of the antenna and df is the far-field distance. The far-field distance is the distance from the transmitting antenna to the beginning of the Fraunhofer region, or far field.

#### Transition zone

The "transition zone" between these near and far field regions, extending over the distance from one to two wavelengths from the antenna[citation needed], is the intermediate region in which both near-field and far-field effects are important. In this region, near-field behavior dies out and ceases to be important, leaving far-field effects as dominant interactions. The image above-right shows these regions and boundaries.

### Regions according to diffraction behavior

Near and far field regions for an antenna larger (diameter or length D) than the wavelength of the radiation it emits, so that Dλ ≫ 1. Examples are radar dishes and other highly directional antennas.

#### Far-field diffraction

If the source has a maximum overall dimension or aperture width (D) that is large compared to the wavelength λ, the far-field region is commonly taken to exist at distances from the source, greater than Fresnel parameter S = D2∕(4λ), S > 1.

For a beam focused at infinity, the far-field region is sometimes referred to as the "Fraunhofer region". Other synonyms are "far-field", "far-zone", and "radiation field". Any electromagnetic radiation consists of an electric field component E and a magnetic field component H. In the far-field, the relationship between the electric field component E and the magnetic component H is that characteristic of any freely propagating wave, where (in units where c = 1) E and H have equal magnitudes at any point in space.

#### Near-field diffraction

In contrast to the far-field, the diffraction pattern in the near-field typically differs significantly from that observed at infinity and varies with distance from the source. In the near-field, the relationship between E and H becomes very complex. Also, unlike the far-field where electromagnetic waves are usually characterized by a single polarization type (horizontal, vertical, circular, or elliptical), all four polarization types can be present in the near-field.[3]

The "near-field", which is inside about one wavelength distance[citation needed] from the antenna, is a region in which there are strong inductive and capacitative effects from the currents and charges in the antenna that cause electromagnetic components that do not behave like far-field radiation. These effects decrease in power far more quickly with distance than do the far-field radiation effects.

Also, in the part of the near-field closest to the antenna (called the "reactive near-field", see below), absorption of electromagnetic power in the region by a second device has effects that feed-back to the transmitter, increasing the load on the transmitter that feeds the antenna by decreasing the antenna impedance that the transmitter "sees". Thus, the transmitter can sense that power has been absorbed from the closest near-field zone, but if this power is not absorbed by another antenna, the transmitter does not supply as much power to the antenna, nor does it draw as much from its own power supply.

#### Variations within regions

The above defined regions categorize field behaviors that vary, even within the region of interest. Thus, the boundaries for these regions are approximate "rules of thumb", as there are no precise cutoffs between them (all behavioral changes with distance are smooth changes). Even when precise boundaries can be defined in some cases, based primarily on antenna type and antenna size, experts may differ in their use of nomenclature to describe the regions.

## Near-field characteristics

The near-field itself is further divided into the reactive near-field and the radiative near-field. The "reactive" and "radiative" near-field designations are also a function of wavelength (or distance). However, these boundary regions are a fraction of one wavelength within the near-field. The outer boundary of the reactive near-field region is commonly considered to be a distance of 1∕2π times the wavelength (λ∕2π or 0.159 × λ) from the antenna surface. The radiative near-field (also called the "Fresnel region") covers the remainder of the near-field region, from λ∕2π out to λ (one full wavelength).[3]

### Reactive near-field, or the nearest part of the near-field

In the reactive near-field (very close to the antenna), the relationship between the strengths of the E and H fields is often too complex to predict. Either field component (E or H) may dominate at one point, and the opposite relationship dominate at a point only a short distance away. This makes finding the true power density in this region problematic. This is because to calculate power, not only E and H both have to be measured but the phase relationship between E and H must also be known.[3]

In this reactive region, not only is an electromagnetic wave being radiated outward into far-space but there is a "reactive" component to the electromagnetic field, meaning that the nature of the field around the antenna is sensitive to, and reacts to, EM absorption in this region (this is not true for absorption far from the antenna, which has no effect on the transmitter or antenna near-field).

Very close to the antenna, in the reactive region, energy of a certain amount, if not absorbed by a receiver, is held back and is stored very near the antenna surface. This energy is carried back and forth from the antenna to the reactive near-field by electromagnetic radiation of the type that slowly changes electrostatic and magnetostatic effects. For example, current flowing in the antenna creates a purely magnetic component in the near-field, which then collapses as the antenna current begins to reverse, causing transfer of the field's magnetic energy back to electrons in the antenna as the changing magnetic field causes a self-inductive effect on the antenna that generated it. This returns energy to the antenna in a regenerative way, so that it is not lost. A similar process happens as electric charge builds up in one section of the antenna under the pressure of the signal voltage, and causes a local electric field around that section of antenna, due to the antenna's self-capacitance. When the signal reverses so that charge is allowed to flow away from this region again, the built-up electric field assists in pushing electrons back in the new direction of their flow, as with the discharge of any unipolar capacitor. This again transfers energy back to the antenna current.

Because of this energy storage and return effect, if either of the inductive or electrostatic effects in the reactive near-field transfers any field energy to electrons in a different (nearby) conductor, then this energy is lost to the primary antenna. When this happens, an extra drain is seen on the transmitter, resulting from the reactive near-field energy that is not returned. This effect shows up as a different impedance in the antenna, as seen by the transmitter.

The reactive component of the near-field can give ambiguous or undetermined results when attempting measurements in this region. In other regions, the power density is inversely proportional to the square of the distance from the antenna. In the vicinity very close to the antenna, however, the energy level can rise dramatically with only a small decrease in distance toward the antenna. This energy can adversely affect both humans and measurement equipment because of the high powers involved.[3]

### Radiative near-field (Fresnel region), or farthest part of the near-field

The radiative near-field (sometimes called the Fresnel region) does not contain reactive field components from the source antenna, since it is so far from the antenna that back-coupling of the fields becomes out-of-phase with the antenna signal, and thus cannot efficiently store and replace inductive or capacitative energy from antenna currents or charges. The energy in the radiative near-field is thus all radiant energy, although its mixture of magnetic and electric components are still different from the far-field. Further out into the radiative near-field (one half wavelength to 1 wavelength from the source), the E and H field relationship is more predictable, but the E to H relationship is still complex. However, since the radiative near-field is still part of the near-field, there is potential for unanticipated (or adverse) conditions.

For example, metal objects such as steel beams can act as antennas by inductively receiving and then "re-radiating" some of the energy in the radiative near-field, forming a new radiating surface to consider. Depending on antenna characteristics and frequencies, such coupling may be far more efficient than simple antenna reception in the yet-more-distant far-field, so far more power may be transferred to the secondary "antenna" in this region than would be the case with a more distant antenna. When a secondary radiating antenna surface is thus activated, it then creates its own near-field regions, but the same conditions apply to them.[3]

### Compared to the far-field

The near-field is remarkable for reproducing classical electromagnetic induction and electric charge effects on the EM field, which effects "die-out" with increasing distance from the antenna (with magnetic field strength proportional to the inverse-cube of the distance and electric field strength proportional to inverse-square of distance), far more rapidly than do the classical radiated EM far-field (E and B fields proportional simply to inverse-distance). Typically near-field effects are not important farther away than a few wavelengths of the antenna.

Far near-field effects also involve energy transfer effects that couple directly to receivers near the antenna, affecting the power output of the transmitter if they do couple, but not otherwise. In a sense, the near-field offers energy that is available to a receiver only if the energy is tapped, and this is sensed by the transmitter by means of answering electromagnetic near-fields emanating from the receiver. Again, this is the same principle that applies in induction coupled devices, such as a transformer, which draws more power at the primary circuit, if power is drawn from the secondary circuit. This is different with the far-field, which constantly draws the same energy from the transmitter, whether it is immediately received, or not.

The amplitude of other components of the electromagnetic field close to the antenna may be quite powerful, but, because of more rapid fall-off with distance than 1∕r behavior, they do not radiate energy to infinite distances. Instead, their energies remain trapped in the region near the antenna, not drawing power from the transmitter unless they excite a receiver in the area close to the antenna. Thus, the near-fields only transfer energy to very nearby receivers, and, when they do, the result is felt as an extra power-draw in the transmitter. As an example of such an effect, power is transferred across space in a common transformer or metal detector by means of near-field phenomena (in this case inductive coupling), in a strictly "short-range" effect (i.e., the range within one wavelength of the signal).

## Classical EM modelling

A "radiation pattern" for an antenna, by definition showing only the far-field.

Solving Maxwell's equations for the electric and magnetic fields for a localized oscillating source, such as an antenna, surrounded by a homogeneous material (typically vacuum or air), yields fields that, far away, decay in proportion to 1∕r where r is the distance from the source. These are the radiating fields, and the region where r is large enough for these fields to dominate is the far field.

In general, the fields of a source in a homogeneous isotropic medium can be written as a multipole expansion.[4] The terms in this expansion are spherical harmonics (which give the angular dependence) multiplied by spherical Bessel functions (which give the radial dependence). For large r, the spherical Bessel functions decay as 1∕r, giving the radiated field above. As one gets closer and closer to the source (smaller r), approaching the near-field, other powers of r become significant.

The next term that becomes significant is proportional to 1∕r2 and is sometimes called the induction term.[5][6] It can be thought of as the primarily magnetic energy stored in the field, and returned to the antenna in every half-cycle, through self-induction. For even smaller r, terms proportional to 1∕r3 become significant; this is sometimes called the electrostatic field term and can be thought of as stemming from the electrical charge in the antenna element.

Very close to the source, the multipole expansion is less useful (too many terms are required for an accurate description of the fields). Rather, in the near-field, it is sometimes useful to express the contributions as a sum of radiating fields combined with evanescent fields, where the latter are exponentially decaying with r. And in the source itself, or as soon as one enters a region of inhomogeneous materials, the multipole expansion is no longer valid and the full solution of Maxwell's equations is generally required.

### Antennas

If sinusoidal currents are applied to a structure of some type, electric and magnetic fields will appear in space about that structure. If those fields extend some distance into space the structure is often termed an antenna. Such an antenna can be an assemblage of conductors in space typical of radio devices or it can be an aperture with a given current distribution radiating into space as is typical of microwave or optical devices. The actual values of the fields in space about the antenna are usually quite complex and can vary with distance from the antenna in various ways.

However, in many practical applications, one is interested only in effects where the distance from the antenna to the observer is very much greater than the largest dimension of the transmitting antenna, the equations describing the fields created about the antenna can be simplified by assuming a large separation and dropping all terms that provide only minor contributions to the final field. These simplified distributions have been termed the "far-field" and usually have the property that the angular distribution of energy does not change with distance, however the energy levels still vary with distance and time. Such an angular energy distribution is usually termed an antenna pattern.

Note that, by the principle of reciprocity, the pattern observed when a particular antenna is transmitting is identical to the pattern measured when the same antenna is used for reception. Typically one finds simple relations describing the antenna far field patterns, often involving trigonometric functions or at worst Fourier or Hankel transform relationships between the antenna current distributions and the observed far field patterns. While far-field simplifications are very useful in engineering calculations, this does not mean the near-field functions cannot be calculated, especially using modern computer techniques. An examination of how the near-fields form about an antenna structure can give great insight into the operations of such devices.

### Impedance

The electromagnetic field in the far-field region of an antenna is independent of the type of field radiated by the antenna. The wave impedance is the ratio of the strength of the electric and magnetic fields, which in the far-field are in phase with each other. Thus, the far-field "impedance of free space" is resistive and is given by:

$Z_0 \ \overset{\underset{\mathrm{def}}{}}{=}\ \mu_0 c_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}} = \frac{1}{\varepsilon_0 c_0}$

With the usual approximation for the speed of light in free space c0 = 3 × 108 m∕s gives the frequently used expression:

$Z_0 \approx 120\pi \approx 377\ \Omega$

The electromagnetic field in the near-field region of an electrically small coil antenna is predominantly magnetic. For small values of rλ, the wave impedance of an inductor is low and inductive, at short range being asymptotic to:

$|Z_W| \approx 240\pi^2 \frac r{\lambda} \approx 2370 \frac r{\lambda}$

The electromagnetic field in the near-field region of an electrically short rod antenna is predominantly electric. For small values of rλ, the wave impedance is high and capacitive, at short range being asymptotic to:

$|Z_W| \approx 60 \frac {\lambda}r$

In both cases, the wave impedance converges on that of free space as the range approaches the far field.[7]

## Quantum field theory view

In the quantum view of electromagnetic interactions, far-field effects are manifestations of real photons, whereas near-field effects are due to a mixture of real and virtual photons. Virtual photons composing near-field fluctuations and signals, have effects that are of far shorter range than those of real photons.

Local effects
Other

## References

1. ^ Acoustic waves: devices, imaging, and analog signal processing, G.Kino, Ed. Prentice Hall (2000) Ch. 3 p. 165
2. ^ Rappaport, Theodore S. Wireless Communications Principles and Practice Second Edition. Prentice-Hall, Inc. 19th Printing, 2010, p. 108.